In general, neither of the steps 1–3 is computational negligible, and each of these steps has to be repeated to
obtain a solution for a new \(\mu \in \mathcal {P}\) .
Note that step 1 requires computations on the fine-scale level whereas steps 2 and 3 solely depend on the size of the coarse mesh \(\mathcal {T}_H\) .
In [1]}, RB approximations of the local corrector problems were introduced to obtain a model that is
independent from the size of \(\mathcal {T}_h\) .
However, for large \(\mathcal {T}_H\) , the costs of solving the reduced corrector problems in step 1 and the further computations
in steps 2 and 3 still can be significant.
The two-scale reduction approach introduced in this work takes all computational steps into account and yields a
reduced order model that is independent from the sizes of both \(\mathcal {T}_h\)  and \(\mathcal {T}_H\) .
